Large language models (LLMs) have been shown to memorize portions of their training data, posing threats to privacy and copyright protection. Many previous studies have attempted to define memorization in a practical way to enable scalable detection. In this work, we investigate compressive memorization and address its key limitation--computational inefficiency. To this end, we propose the adversarial sparsity ratio (ASR) as a proxy for compressive memorization. ASR identifies sparse soft prompts that reconstruct target sequences, enabling a more computationally tractable assessment of memorization. Empirically, we show that ASR effectively distinguishes between memorized and non-memorized content, both within and across models. Furthermore, beyond verbatim memorization, ASR also captures memorization of underlying knowledge, offering a scalable and interpretable tool for analyzing memorization in LLMs.